Computational efficiency improvement of the Universal Line Model by use of rational approximations with real poles

Alternative method using recursive convolution for electromagnetic transient analysis in balanced overhead transmission lines

“…In this model, the differential equations of the currents and voltages of a TL, described in the time domain, are converted into hyperbolic equations in the frequency domain by applying the Laplace transform. In the ULM, the frequency-dependent effects on the parameters of the TL may be taken into account [9][10][11]. Then, the currents and voltages are calculated in the time domain using rational functions obtained by fitting techniques, such as vector fitting and recursive convolutions.…”

“…The ULM synthesises a multi-conductor TL (MTL) by means of its characteristic admittance matrix Y c and its propagation function matrix H. Then, it proceeds to fit both matrices to rational functions and solve them in the time domain using recursive methods [9][10][11]. The accuracy in the ULM is based on the previously identified and extracted modal travel times to fit accurately the rational functions of the propagation matrix H [9][10][11][12][13][14][15]. The modal propagation times can be estimated using several methods e.g.…”

“…The modal propagation times can be estimated using several methods e.g. Bode's formula [11] or Brent's method [13]. The modal travelling times of the propagation function matrix H are estimated based on the identification of the minimum phase method [13].…”

Rational Fitting Techniques for the Modeling of Electric Power Components and Systems Using MATLAB Environment

“…The ULM is formulated in terms of rational approximation of the line parameters through VF. A recent publication, in 2016, [12] Bañuelos et al propose the use of only real poles and zeroes in the ULM to improve its numerical efficiency.…”

“…where Y n is given by By using the Numerical inversion of Laplace Transform (NLT) [2,12], the voltage responses on time domain (v 1 , v 2 and v 3 ) are calculated for the cases of open-ended, short-circuited, and perfectly matched lines end. These results are considered as a reference solution.…”